Britain was a key part of the unit, dubbed by some a European Army, and was set to supply the majority of the 1,500 soldiers for a six month spell in the second half of 2019.
Brexit negotiations officially started on June 19, when UK Brexit Secretary David Davis arrived in Brussels to negotiate the terms with EU's chief negotiator Michel Barnier.
The negotiations are expected to include discussion of Britain's role within the EU battlegroup, but military sources have reportedly already signed up to the idea in principle.
Each of the 28 EU countries takes it in turns to provide the bulk of the troops for the unit and Britain's turn comes in July 2019. Spain is currently providing the bulk of the unit's forces.
The battlegroup, which was designed for peacekeeping or crisis resolution tasks, has not yet been deployed in a real-life event.
How would a 6-month rotating "leadership" work in a combat situation? What happens if the changeover takes place mid-deployment? 🤔— Angry (@WMLabourVoter) July 4, 2017
It was created in 2005, several years after the conflict in Kosovo, and has yet to see action.
In June, the European Council agreed a new and fairer way to finance the battlegroup.
But many British politicians and army commanders have criticized the concept and felt it was unnecessary when Britain is already a full member of NATO.
"The exact nature of our EU relationship and commitments post 2019 are to be determined as part of the Brexit negotiations. Until then we will continue to play a full and active part in EU discussions and we will remain committed to European peace security after we leave the EU in 2019," said a UK Ministry of Defence spokesman.
Britain is also involved in several other EU military missions.
The Royal Navy leads the Atalanta mission against piracy off the coast of Somalia, which is headed up from a base at Northwood, near London.
British sailors are also involved in Operation Sophia, the Italian-commanded operation to combat migrant trafficking in the Mediterranean.